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The von Neumann/Morgenstern approach to ambiguity

  • Martin Dumav

    ()

    (Center for Mathematical Economics, Bielefeld University)

  • Maxwell B. Stinchcombe

    ()

    (Department of Economics, University of Texas, Austin)

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    A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: first and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-480.pdf
    File Function: First version, 2013
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    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 480.

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    Length: 38 pages
    Date of creation: May 2013
    Date of revision:
    Handle: RePEc:bie:wpaper:480
    Contact details of provider: Postal: Postfach 10 01 31, 33501 Bielefeld
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    Web page: http://www.imw.uni-bielefeld.de/

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    1. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
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    5. Marciano Siniscalchi, 2003. "A Behavioral Characterization of Plausible Priors," Discussion Papers 1365, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130179, HAL.
    7. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
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    9. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
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    11. AMARANTE, Massimiliano, 2009. "Analogy in Decision-Making," Cahiers de recherche 14-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    12. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
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    14. Chew, Soo Hong & Epstein, Larry G. & Zilcha, Itzhak, 1988. "A correspondence theorem between expected utility and smooth utility," Journal of Economic Theory, Elsevier, vol. 46(1), pages 186-193, October.
    15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    16. Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
    17. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
    18. Maxwell B. Stinchcombe, 1994. "Countably Additive Subjective Probabilities," CARE Working Papers 9403, The University of Texas at Austin, Center for Applied Research in Economics.
    19. Stigler, George J & Becker, Gary S, 1977. "De Gustibus Non Est Disputandum," American Economic Review, American Economic Association, vol. 67(2), pages 76-90, March.
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